This paper describes a two-pass algorithm capable of computing solutions to the global illumination in general environments (diffuse or glossy surfaces, anisotropically scattering participating media) faster than previous methods, by combining the strengths of finite element and Monte Carlo methods. A quick coarse solution is first computed with a clustered directional hierarchical method. This intermediate solution is used by a Monte Carlo method to accelerate computation of a final accurate solution by importance sampling, by means of Link Probabilities and adaptive probability density functions. Results from a first implementation of the algorithm for diffuse surfaces are presented.